Question

At the centre of a fixed large circular coil of radius $R$, a much smaller circular coil of radius $r$ is placed. The two coils are concentric and are in the same plane. The larger coil carries a current $I$. The smaller coil is set to rotate with a constant angular velocity $\omega$ about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time $t$ of its start of rotation.

• A. $\frac{{\mu }_{0}I}{2R}\omega r^2\sin \omega t$
• B. $\frac{{\mu }_{0}I}{4R}\omega \pi r^2\sin \omega t$
• C. $\frac{{\mu }_{0}I}{2R}\omega \pi r^2\sin \omega t$
• D. $\frac{{\mu }_{0}I}{4R}\omega r^2\sin \omega t$

Answer 1

The correct option is C $\frac{{\mu }_{0}I}{2R}\omega \pi r^2\sin \omega t$

$\varphi =\overline{B}.\overline{A}=BA\cos wt=\pi r^{2}b\cos wt$

$\in =-\frac{d\varphi }{dt}$

$=-\frac{d}{dt}\left(\pi r^{2}B\cos wt\right)$

$=\pi r^{2}B\sin wt\left(w\right)$

$=\frac{{\mu }_{o}I}{2R}\pi w{r}^2\sin wt$ $(\therefore B=\frac{{\mu }_{o}I}{2R})$